Simplify; express your answer in exponential form. Assume $p\neq 0, z\neq 0$. $\dfrac{{(p^{-1})^{-1}}}{{(p^{-5}z^{5})^{3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{-1}}$ to the exponent ${-1}$ . Now ${-1 \times -1 = 1}$ , so ${(p^{-1})^{-1} = p}$ In the denominator, we can use the distributive property of exponents. ${(p^{-5}z^{5})^{3} = (p^{-5})^{3}(z^{5})^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{-1})^{-1}}}{{(p^{-5}z^{5})^{3}}} = \dfrac{{p}}{{p^{-15}z^{15}}}$ Break up the equation by variable and simplify. $\dfrac{{p}}{{p^{-15}z^{15}}} = \dfrac{{p}}{{p^{-15}}} \cdot \dfrac{{1}}{{z^{15}}} = p^{{1} - {(-15)}} \cdot z^{- {15}} = p^{16}z^{-15}$.